Ab initiocalculations of Hc2 in type-II superconductors: Basic formalism and model calculations

Detailed Fermi-surface structures are essential to describe the upper critical field ${H}_{c2}$ in type-II superconductors, as first noticed by and Hohenberg and Werthamer [Phys. Rev. 153, 493 (1967)] and shown explicitly by Butler for high-purity cubic Niobium [Phys. Rev. Lett. 44, 1516 (1980)]. We derive an ${H}_{c2}$ equation for classic type-II superconductors that is applicable to systems with anisotropic Fermi surfaces and/or energy gaps under arbitrary field directions. It can be solved efficiently by using Fermi surfaces from ab initio electronic-structure calculations. Thus, it is expected to enhance our quantitative understanding on ${H}_{c2}$. Based on the formalism, we calculate ${H}_{c2}$ curves for Fermi surfaces of a three-dimensional tight-binding model with cubic symmetry, an isotropic gap, and no impurity scatterings. It is found that, as the Fermi surface approaches to the Brillouin zone boundary, the reduced critical field $h*(T∕{T}_{c})$, which is normalized by the initial slope at ${T}_{c}$, is enhanced significantly over the curve for the spherical Fermi surface with a marked upward curvature. Thus, the Fermi-surface anisotropy can be a main source of the upward curvature in ${H}_{c2}$ near ${T}_{c}$.